Question

a data set 20, 36, 52, 56, 24, 16, 40, 4, 28 represents the number of books purchased by nine book - club members in a year. construct a box plot for these data on the number line below.

Explanation:

Step1: Order the data

$4,16,20,24,28,36,40,52,56$

Step2: Find the median (Q2)

Since there are 9 data - points, the median is the 5th value. So, $Q2 = 28$.

Step3: Find the lower half of data

The lower half is $4,16,20,24$. The median of the lower half (Q1) is $\frac{16 + 20}{2}=18$.

Step4: Find the upper half of data

The upper half is $36,40,52,56$. The median of the upper half (Q3) is $\frac{40+52}{2} = 46$.

Step5: Identify the minimum and maximum

The minimum value is $4$ and the maximum value is $56$.

Step6: Draw the box - plot

On the number line, mark the minimum ($4$), Q1 ($18$), Q2 ($28$), Q3 ($46$), and maximum ($56$). Draw a box from Q1 to Q3 with a vertical line at Q2. Draw whiskers from the box to the minimum and maximum values.

Answer:

A box - plot is constructed with minimum = 4, Q1 = 18, Q2 = 28, Q3 = 46, maximum = 56.